# Properties

 Label 751.2 Level 751 Weight 2 Dimension 23126 Nonzero newspaces 8 Newforms 11 Sturm bound 94000 Trace bound 1

## Defining parameters

 Level: $$N$$ = $$751$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$8$$ Newforms: $$11$$ Sturm bound: $$94000$$ Trace bound: $$1$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(751))$$.

Total New Old
Modular forms 23875 23875 0
Cusp forms 23126 23126 0
Eisenstein series 749 749 0

## Trace form

 $$23126q - 372q^{2} - 371q^{3} - 368q^{4} - 369q^{5} - 363q^{6} - 367q^{7} - 360q^{8} - 362q^{9} + O(q^{10})$$ $$23126q - 372q^{2} - 371q^{3} - 368q^{4} - 369q^{5} - 363q^{6} - 367q^{7} - 360q^{8} - 362q^{9} - 357q^{10} - 363q^{11} - 347q^{12} - 361q^{13} - 351q^{14} - 351q^{15} - 344q^{16} - 357q^{17} - 336q^{18} - 355q^{19} - 333q^{20} - 343q^{21} - 339q^{22} - 351q^{23} - 315q^{24} - 344q^{25} - 333q^{26} - 335q^{27} - 319q^{28} - 345q^{29} - 303q^{30} - 343q^{31} - 312q^{32} - 327q^{33} - 321q^{34} - 327q^{35} - 284q^{36} - 337q^{37} - 315q^{38} - 319q^{39} - 285q^{40} - 333q^{41} - 279q^{42} - 331q^{43} - 291q^{44} - 297q^{45} - 303q^{46} - 327q^{47} - 251q^{48} - 318q^{49} - 282q^{50} - 303q^{51} - 277q^{52} - 321q^{53} - 255q^{54} - 303q^{55} - 255q^{56} - 295q^{57} - 285q^{58} - 315q^{59} - 207q^{60} - 313q^{61} - 279q^{62} - 271q^{63} - 248q^{64} - 291q^{65} - 231q^{66} - 307q^{67} - 249q^{68} - 279q^{69} - 231q^{70} - 303q^{71} - 180q^{72} - 301q^{73} - 261q^{74} - 251q^{75} - 235q^{76} - 279q^{77} - 207q^{78} - 295q^{79} - 189q^{80} - 254q^{81} - 249q^{82} - 291q^{83} - 151q^{84} - 267q^{85} - 243q^{86} - 255q^{87} - 195q^{88} - 285q^{89} - 141q^{90} - 263q^{91} - 207q^{92} - 247q^{93} - 231q^{94} - 255q^{95} - 123q^{96} - 277q^{97} - 204q^{98} - 219q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(751))$$

We only show spaces with even parity, since no modular forms exist when this condition is not satisfied. Within each space $$S_k^{\mathrm{new}}(N, \chi)$$ we list the newforms together with their dimension.

Label $$\chi$$ Newforms Dimension $$\chi$$ degree
751.2.a $$\chi_{751}(1, \cdot)$$ 751.2.a.a 24 1
751.2.a.b 38
751.2.c $$\chi_{751}(72, \cdot)$$ 751.2.c.a 124 2
751.2.d $$\chi_{751}(80, \cdot)$$ 751.2.d.a 4 4
751.2.d.b 4
751.2.d.c 236
751.2.g $$\chi_{751}(76, \cdot)$$ 751.2.g.a 496 8
751.2.h $$\chi_{751}(51, \cdot)$$ 751.2.h.a 1220 20
751.2.k $$\chi_{751}(32, \cdot)$$ 751.2.k.a 2480 40
751.2.l $$\chi_{751}(8, \cdot)$$ 751.2.l.a 6100 100
751.2.o $$\chi_{751}(2, \cdot)$$ 751.2.o.a 12400 200